83 citations · 489 across the 11 of their papers we have counts for
7 papers · 1 filter
Tunneling resonances in systems without a classical trapping
D. Borisov, P. Exner, A. Golovina
In this paper we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths separated by a window of lengt…
On the critical exponent in an isoperimetric inequality for chords
Pavel Exner, Martin Fraas, Evans M. Harrell
The problem of maximizing the norms of chords connecting points on a closed curve separated by arclength arises in electrostatic and quantum--mechanical problems. It is k…
Exponential splitting of bound states in a waveguide with a pair of distant windows
D. Borisov, P. Exner
We consider Laplacian in a straight planar strip with Dirichlet boundary which has two Neumann ``windows'' of the same length the centers of which are apart, and study the asy…
Leaky quantum graphs: approximations by point interaction Hamiltonians
P. Exner, K. Nemcova
We prove an approximation result showing how operators of the type in , where is a graph, can be modeled in the strong resolvent sense by point-…
Topologically non-trivial quantum layers
G. Carron, P. Exner, D. Krejcirik
Given a complete non-compact surface embedded in R^3, we consider the Dirichlet Laplacian in a layer of constant width about the surface. Using an intrinsic approach to the layer g…
Bound States in Curved Quantum Layers
Pierre Duclos, Pavel Exner, David Krejcirik
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in . We suppose that the latter is end…